\(\int \frac {12 x+e^{15} (-4+4 x)+e^5 (-12+12 x-8 x^2)+e^{10} (12 x-8 x^2)+(-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 (24 x-16 x^2)) \log (x)+(12 x-8 x^2+e^5 (-12+12 x)) \log ^2(x)+(-4+4 x) \log ^3(x)}{(10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} (6 x+4 x^3)+(4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 (12 x+8 x^3)) \log (x)+(6 x+6 e^{10} x-12 e^5 x^2+4 x^3) \log ^2(x)+(4 e^5 x-4 x^2) \log ^3(x)+x \log ^4(x)) \log (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} (6+4 x^2)+(4 e^{15}-12 x-12 e^{10} x+e^5 (12+8 x^2)) \log (x)+(6+6 e^{10}-12 e^5 x+4 x^2) \log ^2(x)+(4 e^5-4 x) \log ^3(x)+\log ^4(x))} \, dx\) [2726]

Optimal result

Integrand size = 337, antiderivative size = 32 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=\log \left (\frac {1}{e \log \left (1+\left (3-x^2+\left (-e^5+x-\log (x)\right )^2\right )^2\right )}\right ) \] Output:

ln(exp(-1)/ln(1+(3+(x-ln(x)-exp(5))^2-x^2)^2))
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(101\) vs. \(2(32)=64\).

Time = 0.08 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.16 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\log \left (\log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+4 \left (e^{15}-3 x-3 e^{10} x+e^5 \left (3+2 x^2\right )\right ) \log (x)+2 \left (3+3 e^{10}-6 e^5 x+2 x^2\right ) \log ^2(x)+4 \left (e^5-x\right ) \log ^3(x)+\log ^4(x)\right )\right ) \] Input:

Integrate[(12*x + E^15*(-4 + 4*x) + E^5*(-12 + 12*x - 8*x^2) + E^10*(12*x 
- 8*x^2) + (-12 + 12*x - 8*x^2 + E^10*(-12 + 12*x) + E^5*(24*x - 16*x^2))* 
Log[x] + (12*x - 8*x^2 + E^5*(-12 + 12*x))*Log[x]^2 + (-4 + 4*x)*Log[x]^3) 
/((10*x + E^20*x - 12*E^5*x^2 - 4*E^15*x^2 + E^10*(6*x + 4*x^3) + (4*E^15* 
x - 12*x^2 - 12*E^10*x^2 + E^5*(12*x + 8*x^3))*Log[x] + (6*x + 6*E^10*x - 
12*E^5*x^2 + 4*x^3)*Log[x]^2 + (4*E^5*x - 4*x^2)*Log[x]^3 + x*Log[x]^4)*Lo 
g[10 + E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + (4*E^15 - 12*x - 12 
*E^10*x + E^5*(12 + 8*x^2))*Log[x] + (6 + 6*E^10 - 12*E^5*x + 4*x^2)*Log[x 
]^2 + (4*E^5 - 4*x)*Log[x]^3 + Log[x]^4]),x]
 

Output:

-Log[Log[10 + E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + 4*(E^15 - 3* 
x - 3*E^10*x + E^5*(3 + 2*x^2))*Log[x] + 2*(3 + 3*E^10 - 6*E^5*x + 2*x^2)* 
Log[x]^2 + 4*(E^5 - x)*Log[x]^3 + Log[x]^4]]
 

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {e^5 \left (-8 x^2+12 x-12\right )+e^{10} \left (12 x-8 x^2\right )+\left (-8 x^2+12 x+e^5 (12 x-12)\right ) \log ^2(x)+\left (-8 x^2+e^5 \left (24 x-16 x^2\right )+12 x+e^{10} (12 x-12)-12\right ) \log (x)+12 x+e^{15} (4 x-4)+(4 x-4) \log ^3(x)}{\left (e^{10} \left (4 x^3+6 x\right )-4 e^{15} x^2-12 e^5 x^2+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+\left (4 x^3-12 e^5 x^2+6 e^{10} x+6 x\right ) \log ^2(x)+\left (e^5 \left (8 x^3+12 x\right )-12 e^{10} x^2-12 x^2+4 e^{15} x\right ) \log (x)+e^{20} x+10 x+x \log ^4(x)\right ) \log \left (e^{10} \left (4 x^2+6\right )+\left (4 x^2-12 e^5 x+6 e^{10}+6\right ) \log ^2(x)+\left (e^5 \left (8 x^2+12\right )-12 e^{10} x-12 x+4 e^{15}\right ) \log (x)-4 e^{15} x-12 e^5 x+\log ^4(x)+\left (4 e^5-4 x\right ) \log ^3(x)+e^{20}+10\right )} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^5 \left (-8 x^2+12 x-12\right )+e^{10} \left (12 x-8 x^2\right )+\left (-8 x^2+12 x+e^5 (12 x-12)\right ) \log ^2(x)+\left (-8 x^2+e^5 \left (24 x-16 x^2\right )+12 x+e^{10} (12 x-12)-12\right ) \log (x)+12 x+e^{15} (4 x-4)+(4 x-4) \log ^3(x)}{\left (e^{10} \left (4 x^3+6 x\right )-4 e^{15} x^2-12 e^5 x^2+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+\left (4 x^3-12 e^5 x^2+6 e^{10} x+6 x\right ) \log ^2(x)+\left (e^5 \left (8 x^3+12 x\right )-12 e^{10} x^2-12 x^2+4 e^{15} x\right ) \log (x)+\left (10+e^{20}\right ) x+x \log ^4(x)\right ) \log \left (e^{10} \left (4 x^2+6\right )+\left (4 x^2-12 e^5 x+6 e^{10}+6\right ) \log ^2(x)+\left (e^5 \left (8 x^2+12\right )-12 e^{10} x-12 x+4 e^{15}\right ) \log (x)-4 e^{15} x-12 e^5 x+\log ^4(x)+\left (4 e^5-4 x\right ) \log ^3(x)+e^{20}+10\right )}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {e^5 \left (-8 x^2+12 x-12\right )+e^{10} \left (12 x-8 x^2\right )+\left (-8 x^2+12 x+e^5 (12 x-12)\right ) \log ^2(x)+\left (-8 x^2+e^5 \left (24 x-16 x^2\right )+12 x+e^{10} (12 x-12)-12\right ) \log (x)+12 x+e^{15} (4 x-4)+(4 x-4) \log ^3(x)}{\left (e^{10} \left (4 x^3+6 x\right )+\left (-12 e^5-4 e^{15}\right ) x^2+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+\left (4 x^3-12 e^5 x^2+6 e^{10} x+6 x\right ) \log ^2(x)+\left (e^5 \left (8 x^3+12 x\right )-12 e^{10} x^2-12 x^2+4 e^{15} x\right ) \log (x)+\left (10+e^{20}\right ) x+x \log ^4(x)\right ) \log \left (e^{10} \left (4 x^2+6\right )+\left (4 x^2-12 e^5 x+6 e^{10}+6\right ) \log ^2(x)+\left (e^5 \left (8 x^2+12\right )-12 e^{10} x-12 x+4 e^{15}\right ) \log (x)-4 e^{15} x-12 e^5 x+\log ^4(x)+\left (4 e^5-4 x\right ) \log ^3(x)+e^{20}+10\right )}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {e^5 \left (-8 x^2+12 x-12\right )+e^{10} \left (12 x-8 x^2\right )+\left (-8 x^2+12 x+e^5 (12 x-12)\right ) \log ^2(x)+\left (-8 x^2+e^5 \left (24 x-16 x^2\right )+12 x+e^{10} (12 x-12)-12\right ) \log (x)+12 x+e^{15} (4 x-4)+(4 x-4) \log ^3(x)}{\left (e^{10} \left (4 x^3+6 x\right )+\left (-12 e^5-4 e^{15}\right ) x^2+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+\left (4 x^3-12 e^5 x^2+6 e^{10} x+6 x\right ) \log ^2(x)+\left (e^5 \left (8 x^3+12 x\right )-12 e^{10} x^2-12 x^2+4 e^{15} x\right ) \log (x)+\left (10+e^{20}\right ) x+x \log ^4(x)\right ) \log \left (e^{10} \left (4 x^2+6\right )+\left (4 x^2-12 e^5 x+6 e^{10}+6\right ) \log ^2(x)+\left (e^5 \left (8 x^2+12\right )-12 e^{10} x-12 x+4 e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+\log ^4(x)+\left (4 e^5-4 x\right ) \log ^3(x)+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {4 \log ^3(x)}{x \left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {4 \log ^3(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {8 x \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 e^5 \log ^2(x)}{x \left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 \left (1+e^5\right ) \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {8 \left (1+2 e^5\right ) x \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 \left (1+e^{10}\right ) \log (x)}{x \left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {8 e^5 \left (1+e^5\right ) x}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {12 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 \left (-e^5 \left (2 x^2-3 x+3\right )-\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)+e^{15} (x-1)+3 x-e^{10} x (2 x-3)+(x-1) \log ^3(x)-\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)\right )}{x \left (e^{10} \left (4 x^2+6\right )+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (e^5 \left (2 x^2+3\right )-3 e^{10} x-3 x+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (e^{10} \left (4 x^2+6\right )+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (e^5 \left (2 x^2+3\right )-3 e^{10} x-3 x+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 4 \int -\frac {(1-x) \log ^3(x)+\left (3 e^5 (1-x)-(3-2 x) x\right ) \log ^2(x)+\left (2 x^2-2 e^5 (3-2 x) x-3 x+3 e^{10} (1-x)+3\right ) \log (x)+e^{15} (1-x)-e^{10} (3-2 x) x-3 x+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+e^{20}+10\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+e^{20}+10\right )}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -4 \int \frac {(1-x) \log ^3(x)+\left (3 e^5 (1-x)-(3-2 x) x\right ) \log ^2(x)+\left (2 x^2-2 e^5 (3-2 x) x-3 x+3 e^{10} (1-x)+3\right ) \log (x)+e^{15} (1-x)-e^{10} (3-2 x) x-3 x+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+e^{20}+10\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+e^{20}+10\right )}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle -4 \int \frac {(1-x) \log ^3(x)+\left (3 e^5 (1-x)-(3-2 x) x\right ) \log ^2(x)+\left (2 x^2-2 e^5 (3-2 x) x-3 x+3 e^{10} (1-x)+3\right ) \log (x)+e^{15} (1-x)-e^{10} (3-2 x) x-3 x+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 \left (1+e^{10}\right )\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {\log ^3(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {\log ^3(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5\right ) \log ^2(x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 x \log ^2(x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \log ^2(x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5 \left (2+e^5\right )\right ) \log (x)}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 \left (1+2 e^5\right ) x \log (x)}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^{10}\right ) \log (x)}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 \left (1+e^5+e^{10}+\frac {e^{15}}{3}\right )}{\left (-\log ^4(x)+4 x \log ^3(x)-4 e^5 \log ^3(x)-4 x^2 \log ^2(x)+12 e^5 x \log ^2(x)-6 \left (1+e^{10}\right ) \log ^2(x)-8 e^5 x^2 \log (x)+12 \left (1+e^{10}\right ) x \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)-4 e^{10} x^2+12 e^5 \left (1+\frac {e^{10}}{3}\right ) x-10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {2 e^5 \left (1+e^5\right ) x}{\left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}+\frac {3 e^5 \left (1+\frac {e^{10}}{3}\right )}{x \left (\log ^4(x)-4 x \log ^3(x)+4 e^5 \log ^3(x)+4 x^2 \log ^2(x)-12 e^5 x \log ^2(x)+6 \left (1+e^{10}\right ) \log ^2(x)+8 e^5 x^2 \log (x)-12 \left (1+e^{10}\right ) x \log (x)+12 e^5 \left (1+\frac {e^{10}}{3}\right ) \log (x)+4 e^{10} x^2-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+10 \left (1+\frac {1}{10} e^{10} \left (6+e^{10}\right )\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {-\left ((x-1) \log ^3(x)\right )+\left (x (2 x-3)-3 e^5 (x-1)\right ) \log ^2(x)+\left (2 x^2+2 e^5 (2 x-3) x-3 x-3 e^{10} (x-1)+3\right ) \log (x)-e^{15} (x-1)-3 x+e^{10} x (2 x-3)+e^5 \left (2 x^2-3 x+3\right )}{x \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-12 e^5 \left (1+\frac {e^{10}}{3}\right ) x+e^{10} \left (4 x^2+6\right )+10 \left (1+\frac {e^{20}}{10}\right )\right ) \log \left (\log ^4(x)+4 \left (e^5-x\right ) \log ^3(x)+2 \left (2 x^2-6 e^5 x+3 e^{10}+3\right ) \log ^2(x)+4 \left (-3 e^{10} x-3 x+e^5 \left (2 x^2+3\right )+e^{15}\right ) \log (x)-4 e^5 \left (3+e^{10}\right ) x+2 e^{10} \left (2 x^2+3\right )+10 \left (1+\frac {e^{20}}{10}\right )\right )}dx\)

Input:

Int[(12*x + E^15*(-4 + 4*x) + E^5*(-12 + 12*x - 8*x^2) + E^10*(12*x - 8*x^ 
2) + (-12 + 12*x - 8*x^2 + E^10*(-12 + 12*x) + E^5*(24*x - 16*x^2))*Log[x] 
 + (12*x - 8*x^2 + E^5*(-12 + 12*x))*Log[x]^2 + (-4 + 4*x)*Log[x]^3)/((10* 
x + E^20*x - 12*E^5*x^2 - 4*E^15*x^2 + E^10*(6*x + 4*x^3) + (4*E^15*x - 12 
*x^2 - 12*E^10*x^2 + E^5*(12*x + 8*x^3))*Log[x] + (6*x + 6*E^10*x - 12*E^5 
*x^2 + 4*x^3)*Log[x]^2 + (4*E^5*x - 4*x^2)*Log[x]^3 + x*Log[x]^4)*Log[10 + 
 E^20 - 12*E^5*x - 4*E^15*x + E^10*(6 + 4*x^2) + (4*E^15 - 12*x - 12*E^10* 
x + E^5*(12 + 8*x^2))*Log[x] + (6 + 6*E^10 - 12*E^5*x + 4*x^2)*Log[x]^2 + 
(4*E^5 - 4*x)*Log[x]^3 + Log[x]^4]),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(92\) vs. \(2(30)=60\).

Time = 52.08 (sec) , antiderivative size = 93, normalized size of antiderivative = 2.91

method	result	size
risch	\(-\ln \left (\ln \left (\ln \left (x \right )^{4}+\left (4 \,{\mathrm e}^{5}-4 x \right ) \ln \left (x \right )^{3}+\left (6 \,{\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+4 x^{2}+6\right ) \ln \left (x \right )^{2}+\left (4 \,{\mathrm e}^{15}-12 x \,{\mathrm e}^{10}+\left (8 x^{2}+12\right ) {\mathrm e}^{5}-12 x \right ) \ln \left (x \right )+{\mathrm e}^{20}-4 x \,{\mathrm e}^{15}+\left (4 x^{2}+6\right ) {\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+10\right )\right )\)	\(93\)
parallelrisch	\(-\ln \left (\ln \left (\ln \left (x \right )^{4}+\left (4 \,{\mathrm e}^{5}-4 x \right ) \ln \left (x \right )^{3}+\left (6 \,{\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+4 x^{2}+6\right ) \ln \left (x \right )^{2}+\left (4 \,{\mathrm e}^{15}-12 x \,{\mathrm e}^{10}+\left (8 x^{2}+12\right ) {\mathrm e}^{5}-12 x \right ) \ln \left (x \right )+{\mathrm e}^{20}-4 x \,{\mathrm e}^{15}+\left (4 x^{2}+6\right ) {\mathrm e}^{10}-12 x \,{\mathrm e}^{5}+10\right )\right )\)	\(105\)
default	\(-\ln \left (\ln \left (4 \ln \left (x \right )^{3} {\mathrm e}^{5}-12 x \,{\mathrm e}^{5} \ln \left (x \right )^{2}+8 \,{\mathrm e}^{5} \ln \left (x \right ) x^{2}+\ln \left (x \right )^{4}-4 x \ln \left (x \right )^{3}+4 x^{2} \ln \left (x \right )^{2}+6 \ln \left (x \right )^{2} {\mathrm e}^{10}-12 \ln \left (x \right ) {\mathrm e}^{10} x +4 \,{\mathrm e}^{10} x^{2}+12 \,{\mathrm e}^{5} \ln \left (x \right )-12 x \,{\mathrm e}^{5}+6 \ln \left (x \right )^{2}+4 \ln \left (x \right ) {\mathrm e}^{15}-12 x \ln \left (x \right )-4 x \,{\mathrm e}^{15}+{\mathrm e}^{20}+6 \,{\mathrm e}^{10}+10\right )\right )\)	\(128\)

Input:

int(((-4+4*x)*ln(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*ln(x)^2+((12*x-12)*exp 
(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*x-12)*ln(x)+(-4+4*x)*exp(5)^3+(-8*x^2 
+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*ln(x)^4+(4*x*exp(5)-4*x^2 
)*ln(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*ln(x)^2+(4*x*exp(5)^3-12* 
x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*x^2)*ln(x)+x*exp(5)^4-4*x^2*exp(5)^3+( 
4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/ln(ln(x)^4+(4*exp(5)-4*x)*ln(x)^3+ 
(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*ln(x)^2+(4*exp(5)^3-12*x*exp(5)^2+(8*x^2+ 
12)*exp(5)-12*x)*ln(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*exp(5)^2-12*x*exp(5 
)+10),x,method=_RETURNVERBOSE)
 

Output:

-ln(ln(ln(x)^4+(4*exp(5)-4*x)*ln(x)^3+(6*exp(10)-12*x*exp(5)+4*x^2+6)*ln(x 
)^2+(4*exp(15)-12*x*exp(10)+(8*x^2+12)*exp(5)-12*x)*ln(x)+exp(20)-4*x*exp( 
15)+(4*x^2+6)*exp(10)-12*x*exp(5)+10))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (30) = 60\).

Time = 0.07 (sec) , antiderivative size = 95, normalized size of antiderivative = 2.97 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\log \left (\log \left (-4 \, {\left (x - e^{5}\right )} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 2 \, {\left (2 \, x^{2} - 6 \, x e^{5} + 3 \, e^{10} + 3\right )} \log \left (x\right )^{2} - 4 \, x e^{15} + 2 \, {\left (2 \, x^{2} + 3\right )} e^{10} - 12 \, x e^{5} - 4 \, {\left (3 \, x e^{10} - {\left (2 \, x^{2} + 3\right )} e^{5} + 3 \, x - e^{15}\right )} \log \left (x\right ) + e^{20} + 10\right )\right ) \] Input:

integrate(((-4+4*x)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x 
-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*x-12)*log(x)+(-4+4*x)*exp(5)^ 
3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex 
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x* 
exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x 
^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp(5 
)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x 
*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*e 
xp(5)^2-12*x*exp(5)+10),x, algorithm="fricas")
 

Output:

-log(log(-4*(x - e^5)*log(x)^3 + log(x)^4 + 2*(2*x^2 - 6*x*e^5 + 3*e^10 + 
3)*log(x)^2 - 4*x*e^15 + 2*(2*x^2 + 3)*e^10 - 12*x*e^5 - 4*(3*x*e^10 - (2* 
x^2 + 3)*e^5 + 3*x - e^15)*log(x) + e^20 + 10))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (26) = 52\).

Time = 7.20 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.25 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=- \log {\left (\log {\left (- 4 x e^{15} - 12 x e^{5} + \left (- 4 x + 4 e^{5}\right ) \log {\left (x \right )}^{3} + \left (4 x^{2} + 6\right ) e^{10} + \left (4 x^{2} - 12 x e^{5} + 6 + 6 e^{10}\right ) \log {\left (x \right )}^{2} + \left (- 12 x e^{10} - 12 x + \left (8 x^{2} + 12\right ) e^{5} + 4 e^{15}\right ) \log {\left (x \right )} + \log {\left (x \right )}^{4} + 10 + e^{20} \right )} \right )} \] Input:

integrate(((-4+4*x)*ln(x)**3+((12*x-12)*exp(5)-8*x**2+12*x)*ln(x)**2+((12* 
x-12)*exp(5)**2+(-16*x**2+24*x)*exp(5)-8*x**2+12*x-12)*ln(x)+(-4+4*x)*exp( 
5)**3+(-8*x**2+12*x)*exp(5)**2+(-8*x**2+12*x-12)*exp(5)+12*x)/(x*ln(x)**4+ 
(4*x*exp(5)-4*x**2)*ln(x)**3+(6*x*exp(5)**2-12*x**2*exp(5)+4*x**3+6*x)*ln( 
x)**2+(4*x*exp(5)**3-12*x**2*exp(5)**2+(8*x**3+12*x)*exp(5)-12*x**2)*ln(x) 
+x*exp(5)**4-4*x**2*exp(5)**3+(4*x**3+6*x)*exp(5)**2-12*x**2*exp(5)+10*x)/ 
ln(ln(x)**4+(4*exp(5)-4*x)*ln(x)**3+(6*exp(5)**2-12*x*exp(5)+4*x**2+6)*ln( 
x)**2+(4*exp(5)**3-12*x*exp(5)**2+(8*x**2+12)*exp(5)-12*x)*ln(x)+exp(5)**4 
-4*x*exp(5)**3+(4*x**2+6)*exp(5)**2-12*x*exp(5)+10),x)
 

Output:

-log(log(-4*x*exp(15) - 12*x*exp(5) + (-4*x + 4*exp(5))*log(x)**3 + (4*x** 
2 + 6)*exp(10) + (4*x**2 - 12*x*exp(5) + 6 + 6*exp(10))*log(x)**2 + (-12*x 
*exp(10) - 12*x + (8*x**2 + 12)*exp(5) + 4*exp(15))*log(x) + log(x)**4 + 1 
0 + exp(20)))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 92 vs. \(2 (30) = 60\).

Time = 0.30 (sec) , antiderivative size = 92, normalized size of antiderivative = 2.88 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\log \left (\log \left (-4 \, {\left (x - e^{5}\right )} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 4 \, x^{2} e^{10} + 2 \, {\left (2 \, x^{2} - 6 \, x e^{5} + 3 \, e^{10} + 3\right )} \log \left (x\right )^{2} - 4 \, x {\left (e^{15} + 3 \, e^{5}\right )} + 4 \, {\left (2 \, x^{2} e^{5} - 3 \, x {\left (e^{10} + 1\right )} + e^{15} + 3 \, e^{5}\right )} \log \left (x\right ) + e^{20} + 6 \, e^{10} + 10\right )\right ) \] Input:

integrate(((-4+4*x)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x 
-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*x-12)*log(x)+(-4+4*x)*exp(5)^ 
3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex 
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x* 
exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x 
^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp(5 
)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x 
*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*e 
xp(5)^2-12*x*exp(5)+10),x, algorithm="maxima")
 

Output:

-log(log(-4*(x - e^5)*log(x)^3 + log(x)^4 + 4*x^2*e^10 + 2*(2*x^2 - 6*x*e^ 
5 + 3*e^10 + 3)*log(x)^2 - 4*x*(e^15 + 3*e^5) + 4*(2*x^2*e^5 - 3*x*(e^10 + 
 1) + e^15 + 3*e^5)*log(x) + e^20 + 6*e^10 + 10))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (30) = 60\).

Time = 1.49 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.53 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\log \left (\log \left (8 \, x^{2} e^{5} \log \left (x\right ) + 4 \, x^{2} \log \left (x\right )^{2} - 12 \, x e^{5} \log \left (x\right )^{2} - 4 \, x \log \left (x\right )^{3} + 4 \, e^{5} \log \left (x\right )^{3} + \log \left (x\right )^{4} + 4 \, x^{2} e^{10} - 12 \, x e^{10} \log \left (x\right ) + 6 \, e^{10} \log \left (x\right )^{2} - 4 \, x e^{15} - 12 \, x e^{5} - 12 \, x \log \left (x\right ) + 4 \, e^{15} \log \left (x\right ) + 12 \, e^{5} \log \left (x\right ) + 6 \, \log \left (x\right )^{2} + e^{20} + 6 \, e^{10} + 10\right )\right ) \] Input:

integrate(((-4+4*x)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x 
-12)*exp(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*x-12)*log(x)+(-4+4*x)*exp(5)^ 
3+(-8*x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*ex 
p(5)-4*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x* 
exp(5)^3-12*x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x 
^2*exp(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp(5 
)-4*x)*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x 
*exp(5)^2+(8*x^2+12)*exp(5)-12*x)*log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*e 
xp(5)^2-12*x*exp(5)+10),x, algorithm="giac")
 

Output:

-log(log(8*x^2*e^5*log(x) + 4*x^2*log(x)^2 - 12*x*e^5*log(x)^2 - 4*x*log(x 
)^3 + 4*e^5*log(x)^3 + log(x)^4 + 4*x^2*e^10 - 12*x*e^10*log(x) + 6*e^10*l 
og(x)^2 - 4*x*e^15 - 12*x*e^5 - 12*x*log(x) + 4*e^15*log(x) + 12*e^5*log(x 
) + 6*log(x)^2 + e^20 + 6*e^10 + 10))
 

Mupad [B] (verification not implemented)

Time = 3.60 (sec) , antiderivative size = 95, normalized size of antiderivative = 2.97 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\ln \left (\ln \left ({\ln \left (x\right )}^4+\left (4\,{\mathrm {e}}^5-4\,x\right )\,{\ln \left (x\right )}^3+\left (4\,x^2-12\,{\mathrm {e}}^5\,x+6\,{\mathrm {e}}^{10}+6\right )\,{\ln \left (x\right )}^2+\left (4\,{\mathrm {e}}^{15}-12\,x-12\,x\,{\mathrm {e}}^{10}+{\mathrm {e}}^5\,\left (8\,x^2+12\right )\right )\,\ln \left (x\right )+{\mathrm {e}}^{20}-12\,x\,{\mathrm {e}}^5-4\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^{10}\,\left (4\,x^2+6\right )+10\right )\right ) \] Input:

int((12*x + log(x)^2*(12*x - 8*x^2 + exp(5)*(12*x - 12)) + exp(10)*(12*x - 
 8*x^2) - exp(5)*(8*x^2 - 12*x + 12) + log(x)^3*(4*x - 4) + log(x)*(12*x + 
 exp(5)*(24*x - 16*x^2) - 8*x^2 + exp(10)*(12*x - 12) - 12) + exp(15)*(4*x 
 - 4))/(log(exp(20) + log(x)^2*(6*exp(10) - 12*x*exp(5) + 4*x^2 + 6) - 12* 
x*exp(5) - 4*x*exp(15) + log(x)^4 + exp(10)*(4*x^2 + 6) - log(x)^3*(4*x - 
4*exp(5)) - log(x)*(12*x - 4*exp(15) + 12*x*exp(10) - exp(5)*(8*x^2 + 12)) 
 + 10)*(10*x + x*log(x)^4 + exp(10)*(6*x + 4*x^3) + x*exp(20) + log(x)^3*( 
4*x*exp(5) - 4*x^2) - 12*x^2*exp(5) - 4*x^2*exp(15) + log(x)*(exp(5)*(12*x 
 + 8*x^3) + 4*x*exp(15) - 12*x^2*exp(10) - 12*x^2) + log(x)^2*(6*x + 6*x*e 
xp(10) - 12*x^2*exp(5) + 4*x^3))),x)
 

Output:

-log(log(exp(20) + log(x)^2*(6*exp(10) - 12*x*exp(5) + 4*x^2 + 6) - 12*x*e 
xp(5) - 4*x*exp(15) + log(x)^4 + exp(10)*(4*x^2 + 6) - log(x)^3*(4*x - 4*e 
xp(5)) - log(x)*(12*x - 4*exp(15) + 12*x*exp(10) - exp(5)*(8*x^2 + 12)) + 
10))
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 125, normalized size of antiderivative = 3.91 \[ \int \frac {12 x+e^{15} (-4+4 x)+e^5 \left (-12+12 x-8 x^2\right )+e^{10} \left (12 x-8 x^2\right )+\left (-12+12 x-8 x^2+e^{10} (-12+12 x)+e^5 \left (24 x-16 x^2\right )\right ) \log (x)+\left (12 x-8 x^2+e^5 (-12+12 x)\right ) \log ^2(x)+(-4+4 x) \log ^3(x)}{\left (10 x+e^{20} x-12 e^5 x^2-4 e^{15} x^2+e^{10} \left (6 x+4 x^3\right )+\left (4 e^{15} x-12 x^2-12 e^{10} x^2+e^5 \left (12 x+8 x^3\right )\right ) \log (x)+\left (6 x+6 e^{10} x-12 e^5 x^2+4 x^3\right ) \log ^2(x)+\left (4 e^5 x-4 x^2\right ) \log ^3(x)+x \log ^4(x)\right ) \log \left (10+e^{20}-12 e^5 x-4 e^{15} x+e^{10} \left (6+4 x^2\right )+\left (4 e^{15}-12 x-12 e^{10} x+e^5 \left (12+8 x^2\right )\right ) \log (x)+\left (6+6 e^{10}-12 e^5 x+4 x^2\right ) \log ^2(x)+\left (4 e^5-4 x\right ) \log ^3(x)+\log ^4(x)\right )} \, dx=-\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x \right )^{4}+4 \mathrm {log}\left (x \right )^{3} e^{5}-4 \mathrm {log}\left (x \right )^{3} x +6 \mathrm {log}\left (x \right )^{2} e^{10}-12 \mathrm {log}\left (x \right )^{2} e^{5} x +4 \mathrm {log}\left (x \right )^{2} x^{2}+6 \mathrm {log}\left (x \right )^{2}+4 \,\mathrm {log}\left (x \right ) e^{15}-12 \,\mathrm {log}\left (x \right ) e^{10} x +8 \,\mathrm {log}\left (x \right ) e^{5} x^{2}+12 \,\mathrm {log}\left (x \right ) e^{5}-12 \,\mathrm {log}\left (x \right ) x +e^{20}-4 e^{15} x +4 e^{10} x^{2}+6 e^{10}-12 e^{5} x +10\right )\right ) \] Input:

int(((-4+4*x)*log(x)^3+((12*x-12)*exp(5)-8*x^2+12*x)*log(x)^2+((12*x-12)*e 
xp(5)^2+(-16*x^2+24*x)*exp(5)-8*x^2+12*x-12)*log(x)+(-4+4*x)*exp(5)^3+(-8* 
x^2+12*x)*exp(5)^2+(-8*x^2+12*x-12)*exp(5)+12*x)/(x*log(x)^4+(4*x*exp(5)-4 
*x^2)*log(x)^3+(6*x*exp(5)^2-12*x^2*exp(5)+4*x^3+6*x)*log(x)^2+(4*x*exp(5) 
^3-12*x^2*exp(5)^2+(8*x^3+12*x)*exp(5)-12*x^2)*log(x)+x*exp(5)^4-4*x^2*exp 
(5)^3+(4*x^3+6*x)*exp(5)^2-12*x^2*exp(5)+10*x)/log(log(x)^4+(4*exp(5)-4*x) 
*log(x)^3+(6*exp(5)^2-12*x*exp(5)+4*x^2+6)*log(x)^2+(4*exp(5)^3-12*x*exp(5 
)^2+(8*x^2+12)*exp(5)-12*x)*log(x)+exp(5)^4-4*x*exp(5)^3+(4*x^2+6)*exp(5)^ 
2-12*x*exp(5)+10),x)
 

Output:

 - log(log(log(x)**4 + 4*log(x)**3*e**5 - 4*log(x)**3*x + 6*log(x)**2*e**1 
0 - 12*log(x)**2*e**5*x + 4*log(x)**2*x**2 + 6*log(x)**2 + 4*log(x)*e**15 
- 12*log(x)*e**10*x + 8*log(x)*e**5*x**2 + 12*log(x)*e**5 - 12*log(x)*x + 
e**20 - 4*e**15*x + 4*e**10*x**2 + 6*e**10 - 12*e**5*x + 10))